Download Chapter 26:DC Circuits

I
Chapter 26:DC Circuits
I
26-4 Series and Parallel EMFs;
Battery Charging
EMFs in series in the same direction: total
voltage is the sum of the separate voltages.
I
26-4 Series and Parallel EMFs;
Battery Charging
EMFs in series, opposite direction: total voltage
is the difference, but the lower-voltage battery
is charged.
I
26-4 Series and Parallel EMFs;
Battery Charging
EMFs in parallel only make sense if the voltages
are the same; this arrangement can produce
more current than a single emf.
I
26-4 Series and Parallel EMFs;
Battery Charging
Example 26-10: Jump starting a car.
A good car battery is being used to jump start a car
with a weak battery. The good battery has an emf
of 12.5 V and internal resistance 0.020 Ω. Suppose
the weak battery has an emf of 10.1 V and internal
resistance 0.10 Ω. Each copper jumper cable is 3.0
m long and 0.50 cm in diameter, and can be
attached as shown. Assume the starter motor can be
represented as a resistor Rs = 0.15 Ω. Determine
the current through the starter motor (a) if only the
weak battery is connected to it, and (b) if the good
battery is also connected.
I
26-5 Circuits Containing Resistor
and Capacitor (RC Circuits)
When the switch is closed, the
capacitor will begin to charge.
As it does, the voltage across
it increases, and the current
through the resistor decreases.
I
26-5 Circuits Containing Resistor
and Capacitor (RC Circuits)
To find the voltage as a function of time,
we write the equation for the voltage
changes around the loop:
Since Q = dI/dt, we can integrate to
find the charge as a function of time:
I
26-5 Circuits Containing Resistor
and Capacitor (RC Circuits)
The voltage across the capacitor is VC = Q/C:
The quantity RC that appears in the
exponent is called the time constant of the
circuit:
I
26-5 Circuits Containing Resistor
and Capacitor (RC Circuits)
The current at any time t can be found by
differentiating the charge:
τ = RC
is the time constant
of the RC circuit
I
26-5 Circuits Containing Resistor
and Capacitor (RC Circuits)
Example 26-11: RC circuit, with emf.
The capacitance in the circuit shown is C = 0.30 μF,
the total resistance is 20 kΩ, and the battery emf
is 12 V. Determine (a) the time constant, (b) the
maximum charge the capacitor could acquire, (c) the
time it takes for the charge to reach 99% of this
value, (d) the current I when the charge Q is half
its maximum value, (e) the maximum current, and (f)
the charge Q when the current I is 0.20 its
maximum value.
I
26-5 Circuits Containing Resistor
and Capacitor (RC Circuits)
If an isolated charged capacitor
is connected across a resistor, it
discharges:
Q0 is the maximum charge
I
26-5 Circuits Containing Resistor
and Capacitor (RC Circuits)
Once again, the voltage and current as
a function of time can be found from
the charge:
and
I
Problem 48
48.(II) The RC circuit of Fig. 26–59 (same
as Fig. 26–18a) has R=8.7kΩ and C=3.0µF
The capacitor is at voltage V0 at t=0s
when the switch is closed. How long does it
take the capacitor to discharge to 0.10% of
its initial voltage?
I
26-5 Circuits Containing Resistor and
Capacitor (RC Circuits)
Example 26-12: Discharging RC circuit.
In the RC circuit shown, the battery has fully charged the capacitor, so
Q0 = C E. Then at t = 0 the switch is thrown from position a to b. The
battery emf is 20.0 V, and the capacitance C = 1.02 μF. The current I
is observed to decrease to 0.50 of its initial value in 40 μs. (a) What is
the value of Q, the charge on the capacitor, at t = 0? (b) What is the
value of R at 40 μs? (c) What is Q at t = 60 μs?
I
26-5 Circuits Containing Resistor
and Capacitor (RC Circuits)
Example 26-14: Resistor in a
turn signal.
Estimate the order of magnitude
of the resistor in a turn-signal
circuit.
I
26-7 Ammeters and
Voltmeters
An ammeter measures current; a voltmeter measures
voltage. Both are based on galvanometers, unless they
are digital.
I
The current in a circuit passes through the
ammeter; the ammeter should have low
resistance so as not to affect the current.
I
26-7 Ammeters and Voltmeters
A voltmeter should not affect the voltage
across the circuit element it is measuring;
therefore its resistance should be very large.
I
26-7 Ammeters and
Voltmeters
An ohmmeter measures
resistance; it requires a
battery to provide a current.
I
26-7 Ammeters and
Voltmeters
Summary: How to connect Meters?
An ammeter must be in series with
the current it is to measure;
A voltmeter must be in parallel
with the voltage it is to measure.